Method for likelihood computation in multi-stream HMM based speech recognition

ABSTRACT

A method for speech recognition includes determining active Gaussians related to a first feature stream and a second feature stream by labeling at least one of the first and second streams, and determining active Gaussians co-occurring in the first stream and the second stream based upon joint probability. A number of Gaussians computed is reduced based upon Gaussians already computed for the first stream and a number of Gaussians co-occurring in the second stream. Speech is decoded based on the Gaussians computed for the first and second streams.

BACKGROUND

1. Technical Field

Exemplary embodiments of the present invention relate to speechrecognition, and more particularly to a system and method, which reducesa number of Gaussian calculations needed to increase computationalefficiency in multi-stream speech recognition tasks.

2. Description of the Related Art

Recently, there has been significant interest in the use of multi-streamhidden Markov models (HMMs) for automatic speech recognition (ASR). Forexample, such models have been successfully considered for multi-bandASR, separate static and dynamic acoustic feature modeling, as well asfor audiovisual ASR.

In its application in audio-visual speech recognition, the multi-streamapproach gives rise to an effective paradigm to fuse and model twoseparate information sources carried in the audio and visualobservations. Specifically, it has been demonstrated that multi-streamdecision fusion attains significant improvement in recognition accuracyover the state-of-the-art single-stream based fusion methods, e.g.,hierarchical linear discriminant analysis (HiLDA).

However, the gain in recognition performance is achieved at the cost ofhigher computational complexity due to the separate statistical modelingof the two observation streams. For instance, in the audio-visual ASRsystem described in Potamianos et al., “Recent advances in the automaticrecognition of audio-visual speech:” Proc. IEEE, 91(9): 1306-1326, 2003,the signal processing front end produces audio and visual observationvectors with 60 and 41 dimensions, respectively. In HiLDA fusion, thejoint audio-visual observations of 101 dimensions are projected to a 60dimensional audio-visual feature space, which can be modeled bysingle-stream HMMs with a similar number of Gaussian densities as theaudio only system.

On the other hand, the multi-stream HMMs model each of the twomodalities in its original feature space. Hence, the number of Gaussiancomponents required is roughly doubled in order to preserve the samemodeling resolution in the output densities. For a typical decodingalgorithm, the time complexity is roughly linear with respect to thetotal number of Gaussians in the system. Therefore, without specialtreatment, an audio-visual system based on two-stream HMMs willapproximately command twice the computational load as a comparablesingle-stream system in the recognition stage.

Effectively managing the computational load is needed for thedevelopment of real-time audio-visual ASR systems. Because visualprocessing is expected to take a sizeable portion of the availablecomputing power, it becomes even more imperative to improve theefficiency of algorithms involved in the decoding process, which includelikelihood computation and search.

Algorithms exist for fast evaluation of Gaussians in single-stream HMMs.One class of algorithms exploits the fact that at a given frame, only asmall subset of Gaussian components in the total Gaussian pool aresignificant to the likelihood computations, e.g., the roadmap algorithmand the hierarchical labeling algorithm. Naturally, these algorithms maybe directly applied to each individual stream in the multi-stream HMM.Moreover, the synchronized and parallel nature of the observationstreams in multi-stream HMMs provides a fresh dimension to formulate newapproaches to further improve computational efficiency.

SUMMARY

A method for speech recognition includes determining active Gaussiansrelated to a first feature stream and a second feature stream bylabeling at least one of the first and second streams, and determiningactive Gaussians co-occurring in the first stream and the second streambased upon joint probability. A number of Gaussians computed is reducedbased upon Gaussians already computed for the first stream and a numberof Gaussians co-occurring in the second stream. Speech is decoded basedon the Gaussians computed for the first and second streams.

These and other objects, features and advantages will become apparentfrom the following detailed description of illustrative embodimentsthereof, which is to be read in connection with the accompanyingdrawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a block/flow diagram showing hierarchical labeling of at leastone stream in accordance with illustrative embodiments;

FIG. 2 is a block/flow diagram showing determination of co-occurringGaussians in accordance with illustrative embodiments;

FIG. 3 is a diagram showing a Gaussian co-occurrence map in training inaccordance with illustrative embodiments;

FIG. 4 is a diagram showing a Gaussian co-occurrence map at runtime inaccordance with illustrative embodiments;

FIG. 5 is a block/flow diagram showing a speech recognition system whichemploys multiple streams for speech recognition in accordance withillustrative embodiments;

FIG. 6 are plots of Gaussian usage (SNR=8.5 dB) for (A) an audio-visualfused stream, (B) a visual stream, (C) a combined usage for audio-visualfused (AVf) and visual streams operating independently, and (D) an AVfand visual stream under a co-occurrence framework for audio.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Exemplary embodiments of the present invention provide efficienthandling and evaluation of mixtures of Gaussian densities in HiddenMarkov Models (HMMs). In one embodiment, a system and method estimate aco-occurrence mapping of the Gaussian mixture components that separatelymodel individual streams of a multi-stream system. The methodessentially treats stream pairs in a master/slave fashion, with themaster Gaussian components driving the slave component selection. Inaccordance with these exemplary embodiments, in an audio-visual digitrecognition task, the system/method can achieve significant improvementin decoding efficiency with a minimal degradation in recognitionperformance.

Multi-stream Hidden Markov Models (HMM) may be introduced in the fieldof automatic speech recognition as an alternative to single-streammodeling of sequences of speech informative features. In particular, themulti-stream HMMs may be successful in audio-visual speech recognition,where features extracted from video of the speaker's lips are alsoavailable. However, in contrast to single-stream modeling, themulti-stream HMMs use during decoding becomes computationally intensive,as it needs calculating class-conditional likelihoods of the addedstream observations.

In accordance with particularly useful embodiments, the calculationoverhead is reduced by drastically limiting the number of observationprobabilities computed for the visual stream. The method estimates ajoint co-occurrence mapping of the Gaussian mixture components thatseparately model the audio and visual observations, and usesco-occurrence mapping to select the visual mixture components to beevaluated, given the already selected audio observations. Experimentsusing this scheme are reported herein on a connected-digits audio-visualdatabase, where it demonstrates significant speed gains at decoding withonly about 5% of the visual Gaussian components requiring evaluation, ascompared to the independent evaluation of audio and visual likelihoods.

It should be understood that the elements shown in the FIGS. may beimplemented in various forms of hardware, software or combinationsthereof. Preferably, these elements are implemented in software on oneor more appropriately programmed general-purpose digital computershaving a processor and memory and input/output interfaces.

It is understood that the embodiments described herein include all ofthe hardware and software components needed to employ speech recognitionon a plurality of different platforms and using a plurality of differenttechnologies. For example, systems employing exemplary embodiments ofthe present invention may include an acoustic/video front end, speechrecognition model storage, processors, microphones, speakers, etc.Platforms may include computers, telephones, personal digitalassistants, recording devices, answering machines and the like.

Referring now to the drawings in which like numerals represent the sameor similar elements and initially to FIG. 1, a system/method forhierarchical labeling is illustratively shown. It is to be understoodthat other labeling methods may also be employed. In an HMM, an emissiondensity function of a state is typically parameterized by a mixture ofGaussian densities. The state conditional likelihood of a givenobservation vector x at time t is computed as

$\begin{matrix}{{p( {x❘s} )} = {\sum\limits_{g \in {G{(s)}}}\;{{p( {g❘s} )}{p( {x❘g} )}}}} & (1)\end{matrix}$where G(s) is the set of Gaussians that make up the GMM (GaussianMixture Model) for state s.

As a part of the training process, the complete set of availableGaussian densities is clustered into a search tree in block 10, in whichthe leaves correspond to the individual Gaussians, and a parent node isthe centroid of its children. Thus, levels closer to the root node canbe viewed as lower resolution representations of the feature space. Inthe experiments described in this paper, the trees illustratively havefour levels.

The hierarchical labeling algorithm takes advantage of the sparseness bysurveying the Gaussian pool in multiple resolutions given a featurevector x, in block 12. In block 14, an evaluation of a Gaussian densitycan be carried out on-demand as a state associated with the particularGaussian is invoked; or, alternatively, a set of Gaussians can beprecomputed as soon as the observation is available without regard totheir state membership. For simplicity, the former may be referred to asthe lazy method, and the latter as the eager method. For a system with alarge number of Gaussians, only a small subset of the complete set ofGaussian densities are significant to likelihood computation at anygiven time. Hence, clever exploitation of this sparseness combined withthe eager method yields a very efficient algorithm to compute theconditional likelihoods during decoding.

During decoding (Runtime), for each feature frame, the tree is traversedto identify a subset of active Gaussians, Y. In block 16, based on Y,the conditional likelihood of a state is computed using the followingapproximation

$\begin{matrix}{{p( {x❘s} )} = {\max\limits_{g \in {Y\bigcap{G{(s)}}}}{{p( {g❘s} )}{p( {x❘g} )}}}} & (2)\end{matrix}$If no Gaussian from a state is present in Y, a default floor likelihoodis assigned to that state in block 18.

Referring to FIG. 2, Gaussian co-occurrence is shown in accordance withillustrative embodiments of the present invention. The hierarchicallabeling of FIG. 1 relies on the hierarchical tree to give a list ofactive Gaussian densities for the current observation. A straightforwardapplication of the algorithm to multi-stream HMMs is to consider aseparate tree for each stream and determine the active Gaussians inindependence from other streams. However, even with the highly efficientpruning provided by hierarchical labeling, the task of Gaussiancomputation still accounts for approximately 50% to 70% of the totalrecognition effort in our single-stream ASR system. So, the independenthierarchical labeling scheme may be unsuitable for real-timeimplementation of multi-stream HMMs.

The synchronous, parallel streams in a multi-stream HMM may be employedto model different aspects of the same underlying stochastic process.Therefore, some degrees of inter-stream dependencies may exist among thefeature spaces. Indeed, this leads to the formulation of Gaussianco-occurrence modeling. Particularly, hierarchical labeling ispreferably applied in only one of the streams in block 20, andco-occurrence statistics are used to determine the active Gaussiancomponents for the rest of the streams in block 22.

To simplify discussion, the subsequent derivations are restricted to thetwo-stream case. However, note that the formulation is completelygeneral, and the equations can be readily extended to include more thantwo observation streams.

Given feature vectors from two streams, x₁ from stream 1 and X₂ fromstream 2, the joint probability p(x₁, x₂ |s) for HMM states is computedin block 24. Multi-stream systems may make the assumption that,conditioned on HMM state, the streams are independent. Consequently, thejoint probability is factored as

$\begin{matrix}\begin{matrix}{{p( {x_{1},{x_{2}❘s}} )} = {{p( {x_{1}❘s} )}{p( {x_{2}❘s} )}}} \\{= {\{ {\sum\limits_{g_{1} \in {G_{1}{(s)}}}\;{{p( {g_{1}❘s} )}{p( {x_{1}❘g_{1}} )}}} \} \times}} \\{\{ {\sum\limits_{g_{2} \in {G_{2}{(s)}}}\;{{p( {g_{2}❘s} )}{p( {x_{2}❘g_{2}} )}}} \}}\end{matrix} & (3)\end{matrix}$Under hierarchical labeling (equation 2), equation 3 is approximated as

$\begin{matrix}{{{p( {x_{1},{x_{2}❘s}} )} = {\{ {\max\limits_{g_{1} \in {Y_{1}\bigcap{G_{1}{(s)}}}}{{p( {g_{1}❘s} )}{p( {x_{1}❘g_{1}} )}}} \} \times \{ {\max\limits_{g_{2} \in {Y_{2}\bigcap{G_{2}{(s)}}}}{{p( {g_{2}❘s} )}{p( {x_{2}❘g_{2}} )}}} \}}},} & (4)\end{matrix}$where Y₁ and Y₂ are the Gaussians resulting from the hierarchicallabeling of stream 1 and stream 2, respectively.

In the Gaussian co-occurrence method it is attempted to model theinter-stream dependence, in block 26. This modeling is started byremoving the independence assumption made in equation 3, and rewritingthe state conditional likelihood as

$\begin{matrix}\begin{matrix}{{p( {x_{1},{x_{2}❘s}} )} = {\sum\limits_{g_{1},{g_{2} \in H}}\;{p( {x_{1},g_{1},x_{2},{g_{2}❘s}} )}}} \\{{= {\sum\limits_{g_{1},{g_{2} \in H}}\;{{p( {x_{1},{g_{1}❘s}} )}{p( {x_{2},{g_{2}❘x_{1}},g_{1},s} )}}}},}\end{matrix} & (5)\end{matrix}$where H is the set of all Gaussians belonging to HMMs used for modelingthe two streams. Note that in one embodiment, the Gaussians are notshared across states or streams, and hence, for any given state, onlyGaussians belonging to that state will be effective in the summation.

Let Q₁ ⊂Y₁ be a set of stream 1 Gaussians. The details of how Q₁ isdetermined are discussed below in the experimental results. Using Q₁,the second term in equation 5 is approximated asp(x ₂ ,g ₂ |x ₁ ,g ₁ ,s)≈p(x ₂ ,g ₂ |x ₁ ,Q ₁ ,s)  (6)then the Right Hand Side of equation 6 is further approximated as

$\begin{matrix}{\mspace{65mu}{{p( {x_{2},{g_{2}❘x_{1}},Q_{1},s} )} \approx \{ \begin{matrix}{{p( {x_{2},{g_{2}❘s}} )},{{{{if}\mspace{14mu}{\max\limits_{g_{1}^{\prime} \in Q_{1}}{q( {g_{1}^{\prime},{g_{2}❘x_{1}}} )}}} > t_{1}};}} \\{0,{{otherwise}.}}\end{matrix} }} & (7)\end{matrix}$In equation 7, q(g′₁,g₂|x₁) denotes a distribution modeling the jointoccurrence of Gaussians of stream 1 and stream 2 and t₁ is anempirically determined threshold, in block 27.

In block 28, the number of Gaussians is reduced or limited. Equation 7in essence uses the co-occurrence distribution q(g′₁,g₂|x₁) and set Q₁to limit the number of Gaussians of stream 2 that are evaluated. Forexample, let

$\begin{matrix}{Q_{2} = \{ {g_{2}:{{\max\limits_{g_{1}^{\prime} \in Q_{1}}{q( {g_{1}^{\prime},{g_{2}❘x_{1}}} )}} > t_{1}}} \}} & (8)\end{matrix}$denote the set of Gaussians that are evaluated for stream 2. Controllingthe size of Q₂ is one important way of how to derive primarycomputational savings. Note that distribution q is employed to determineQ₁; it is to be understood that other ways of determining Q₁ may beemployed, for example, using of the probability values from thisdistribution.

Combining equations 5 and 7, and using the maximum approximation tosummation, as was done in equation 2, the following results

$\begin{matrix}{{{p( {x_{1},{x_{2}❘s}} )} = {\{ {\max\limits_{g_{1} \in {Y_{1}\bigcap{G_{1}{(s)}}}}{{p( {g_{1}❘s} )}{p( {x_{1}❘g_{1}} )}}} \} \times \{ {\max\limits_{g_{2} \in {Y_{2}\bigcap{G_{2}{(s)}}}}{{p( {g_{2}❘s} )}{p( {x_{2}❘g_{2}} )}}} \}}},} & (9)\end{matrix}$

From equation 8, the distribution q(g′₁,g₂|x₁) plays a central role inthe amount of computational savings that can be derived from thismethod. This distribution can be modeled asq(g ₁ ,g ₂ |x ₁)=P _(Q) ₁ (g ₁ |x ₁)q(g ₂ |g ₁),  (10)where P_(Q) ₁ (g₁|x₁)_(q)(g₂|g₁) is computed at test time from thelikelihoods p(x₁, g₁) given by hierarchical labeling of stream 1, as

$\begin{matrix}{{P_{Q_{1}}( {g_{1}❘x_{1}} )} = {\frac{p( {x_{1},g_{1}} )}{\sum\limits_{g_{1}^{\prime} \in Q_{1}}\;{p( {x_{1},g_{1}^{\prime}} )}}.}} & (11)\end{matrix}$

The conditional distribution q(g₂|g₁) is computed at training time by“counting” the instances where g₁ occurs in stream 1 together with g₂ instream2. Specifically, it is derived from the empirical expectation

$\begin{matrix}{{{q( {g_{1},g_{2}} )} = {\frac{1}{T}{\sum\limits_{t}\;{{p( {g_{1}❘{x_{1}(t)}} )}{p( {g_{2}❘{x_{2}(t)}} )}}}}},} & (12)\end{matrix}$where |T| is the total number of training feature vectors.

For storage efficiency, in block 30, q(g₂|g₁) may be sorted indescending order and store only a top few g₂ Gaussians for each g₁ andinclude a cutoff to remove extra Gaussians (e.g., rank cutoff in FIG.3). This stored map is referred to as the Gaussian co-occurrence map.

Referring to FIG. 3, a graphical rendering of a Gaussian co-occurrencemap is illustratively shown. Gaussians in stream 1 (g₁) are identifiedwhich co-occur with Gaussians in stream 2 (g₂) to provide a cooccurrencemap, q(g₂|g₁).

At test time, the Gaussian co-occurrence map is used in conjunction withP_(Q) ₁ (g₁|x₁) values, computed according to equation 11. FIG. 4 showsthe use of the co-occurrence map at runtime generating the co-occurrencedistribution of equation 10.

Referring to FIG. 5, a multi-stream audio-visual speech recognitionsystem 100 is shown in accordance with one illustrative embodiment ofthe present invention. A multi-stream configuration may include three ormore streams, e.g., an audio stream (AU), a visual stream (VI), and anaudiovisual fused stream (AVf), implemented using, e.g., the HILDAapproach.

A visual/video front-end 102 in the audio-visual speech recognitionsystem 100 extracts appearance-based features within a region ofinterest (ROI) defined on, e.g., the mouth area of the speaker.

Given the video input, the system 100 first performs face detectionusing a face detector module 104 at frame-level, using e.g., multi-scaletemplate matching based on a distance measure composed of the two-class(face/non-face) Fisher linear discriminant and the error incurred byprojecting the candidate vector to a lower dimensional “face space”obtained through principal component analysis (PCA). Following facedetection, 26 key facial points (e.g., eye corners and mouth corners)are tracked using a tracking module 106, which may employ algorithms,e.g., algorithms reported in Senior, A. W., “Face and feature findingfor face recognition system,” in Proc. Int. Conf. Audio Visual-basedBiometric Person Authentication, pp. 154-159, 1999. The tracking resultsprovide the location, size, and orientation estimates of the mouth.These parameters are subsequently smoothed over time and used todetermine a 64×64-pixel ROI.

The visual features are preferably computed by applying atwo-dimensional separable discrete cosine transform (DCT) to thesub-image defined by the ROI, and retaining the top 100 coefficientswith respect to energy. The resulting vectors then go though a pipelineincluding of intra-frame LDA/MLLT (Linear Discriminant Analysis/MaximumLikelihood Linear Transformation), temporal interpolation, and featuremean normalization in module 108, producing, e.g., a 30-dimensionalfeature stream at 100 Hz. To account for inter-frame dynamics, fifteenconsecutive frames in the stream are joined and subject to anotherLDA/MLLT step to give the final visual feature vectors (VI stream) with41 dimensions.

The basic audio features extracted by an audio front-end 110 arepreferably 24-dimensional Mel-frequency cepstral coefficients. Aftercepstral mean normalization, nine consecutive frames are concatenatedand projected onto a 60-dimensional space through an LDA/MLLT cascade111, generating the AU feature stream.

The AVf features are generated by concatenating, in block 112, the60-dimensional AU and the 41-dimensional VI features and projecting this101-dimensional feature to a 60-dimensional sub-space through LDA/MLLT.

A recognition system 114 uses three-state, left-to-right phonetic HMMswith context-dependent states. The instances of the sub-phonetic statesare identified by growing a decision tree that clusters left and rightcontexts spanning up to five phones on each side. The states arespecified by the terminal nodes of the tree, and the correspondingobservation streams are modeled by mixtures of Gaussian densities withdiagonal covariance matrices. System 114 includes one or more processors115, memory 116 and peripherals 118 as needed.

Experimental Setup

The audio-visual speech recognition system is evaluated on aconnected-digit recognition task using the IBM studio-DIGIT audio-visualdatabase. The corpus includes Hill-face frontal video of 50 subjects,uttering 7 and 10-digit strings. A total of 6.7K utterances wererecorded in a studio environment with uniform background and lighting.The acoustic signal to noise ratio (SNR) of the recorded data ismeasured at 19.5 dB.

The dataset is partitioned into three subsets: a training set including5.4K utterances, a test set with 623 utterances, and a held-out setincluding 663 utterances. To evaluate the recognition performance innoisy environments, two noisy acoustic conditions were simulated byadding random segments of speech babble recordings to the clean speechsamples. The average SNR of all three test conditions are 19.5 dB(original), as well as, 11.5 dB and 8.5 dB (noisy). The HMMs are trainedusing the clean data, based on a context tree with 159 leaves modeled by3.2K Gaussian densities.

Experimental Results

The baseline recognition accuracy of the three individual streams isshown as a function of SNR in the top three rows of table 1. The fourthand fifth rows of this table show results of the traditional independentmulti-stream configurations for AU+VI and AVf+VI pairs.

TABLE 1 Word error rates for single and multi-stream independent, andco-occurrence systems. SNR 19.5 dB 11.5 dB 8.5 dB AU 1.60 13.45 25.78AVf 1.65 9.38 15.98 VI 37.13 37.13 37.13 AVf + VI (Ind.) 1.59 7.85 12.12AU + VI (Ind.) 1.61 8.97 14.10 AVf + VI (Co.) 1.61 7.62 12.06 AU + VI(Co.) 1.46 9.57 16.03

To carry out the co-occurrence experiments, we generated two maps: onewith AU stream 1 and VI as stream 2, and the other with AVf as stream 1and VI as stream 2. These maps were generated from all of 5.4K trainingsentences. During run time, hierarchical labeling of stream 1 was firstcarried out to generate the set Y₁. The set Q₁ was then derived from Y₁by keeping only the Gaussians which attained the max score in equation2. Q₁, in conjunction with the training time co-occurrence maps (FIG. 3)is then used to identify the stream 2 Gaussians that are to be evaluatedin the runtime co-occurrence maps (FIG. 4, equation 8).

Referring to FIG. 6, a normalized histogram of the number of Gaussiansevaluated per feature vector of the AVf stream in panel (A) and for theVI stream in panel (B) are shown. Note that the sharp rise of thehistogram at the trailing edge of (B) is due to absolute cutoffs onnumber of Gaussians that are permitted to be evaluated in a hierarchicallabeler (see e.g., Novak et al., “Efficient hierarchical labeleralgorithm for Gaussian likelihoods computation in resource constrainedspeech recognition systems,”, ICASS 2002,

http://www.research.ibm.com/people/r/rameshg/novak-icassp2002.ps.

Panel (C) shows the histogram of the Gaussian usage for the case ofindependent combination of AVf and VI. The legend numbers in the plotsindicate the mean usage per observation vector.

Note that in addition to measuring the computational load, thesehistograms also serve as an indicator of the Gaussian separability indifferent streams. For instance, a sharper distribution in panel (A) ascompared to that in panel (B) indicates that the AVf stream has a betterdiscrimination between Gaussians than the VI stream. This is in factcorroborated by the significantly lower error rate obtained with the AVfsystem as shown in Table 1.

Panel (D) of FIG. 6 shows the Gaussian usage for the VI stream operatingunder the co-occurrence framework with AVf as stream 1. The drasticreduction in Gaussian usage is evident. Details of the impact onGaussian usage for the AVf and VI streams operating independently andwith co-occurrence as a function of decreasing SNR is shown in Table 2.

TABLE 2 Average number of evaluated Gaussians per frame for the VIstream determined independently or as a slave of the AVf stream,compared with that of the AVf stream. SNR 19.5 dB 11.5 dB 8.5 dB AverageAVf 423 584 623 543 VI Ind. 853 853 853 853 VI Co. 30 48 56 45

On average, a 94.7% reduction in the number of Gaussians evaluated isobtained while maintaining the word error rate of the independent streamresult, as seen by comparing AVf+VI(Ind.) and AVf+VI(Co.) rows of Table1.

A novel system and method for significantly reducing the number ofGaussian likelihood calculations in a multi-stream system throughco-occurrence is disclosed. On an audiovisual digit recognition task, ithas been found that for certain stream pairs large reduction in thenumber of Gaussian evaluations can be achieved without any loss inaccuracy.

Having described preferred embodiments of a system and method forlikelihood computation in multi-stream hmm based audio-visual speechrecognition (which are intended to be illustrative and not limiting), itis noted that modifications and variations can be made by personsskilled in the art in light of the above teachings. It is therefore tobe understood that changes may be made in the particular embodimentsdisclosed which are within the scope and spirit of the invention asoutlined by the appended claims. Having thus described aspects of theinvention, with the details and particularity required by the patentlaws, what is claimed and desired protected by Letters Patent is setforth in the appended claims.

1. A method for speech recognition, comprising the steps of: determiningactive Gaussians related to a first feature stream and a second featurestream by hierarchically labeling at least one of the first and secondstreams by surveying Gaussians in multiple resolutions; determiningactive Gaussians co-occurring in the first stream and the second streambased upon joint probability wherein the first stream includes an audiostream and the second stream includes a video stream; reducing a numberof Gaussians computed for the second stream based upon Gaussians alreadycomputed for the first stream and a number of Gaussians co-occurring inthe second stream; and decoding speech based on the Gaussians computedfor the first and second streams by employing multi-stream hidden Markovmodels.